I choose the Kardashian as a unit both because I like the mitteleuropean feel of the term – like the Ohm or the Roentgen – and because Kardashian is an exemplar of attention disconnected from merit, talent or reason. The Kardashian mentions how much attention is paid, not how much attention is deserved, so naming the unit after someone who is famous for being famous seems appropriate

a free open-source mathematics software system licensed under the GPL. It combines the power of many existing open-source packages into a common Python-based interface.

His Incompleteness Theorems, among the most significant achievements in logic since, perhaps, those of Aristotle, are among the handful of landmark theorems in twentieth century mathematics. His work touched every field of mathematical logic, if it was not in most cases their original stimulus

While the empty set is a standard and widely accepted mathematical concept, it remains an ontological curiosity, whose meaning and usefulness are debated by philosophers and logicians.
The empty set is not the same thing as nothing; rather, it is a set with nothing inside it and a set is always something. This issue can be overcome by viewing a set as a bag—an empty bag undoubtedly still exists. Darling (2004) explains that the empty set is not nothing, but rather "the set of all triangles with four sides, the set of all numbers that are bigger than nine but smaller than eight, and the set of all opening moves in chess that involve a king."

A simplified (and mostly accurate) way to think about this is that every team starts out with an equal number of "quality points".  Every time the computer says "Go", teams distribute their quality points to all the teams that beat them.  Thus, good teams get more quality points than they gave away (and vice versa for bad teams).  After a few rounds of this procedure, the quality points for every team approaches convergence.

Now by comparing the entropy before and after the split, we obtain a measure of information gain, or how much information we gained by doing the split using that particular feature. At each node of the tree, this calculation is done for each feature. And the feature with the largest information gain is chosen for the split. This process continues iteratively until the end.

this particular model is an example of duration analysis. Duration analysis is used in lots of fields, but with different names. Engineers might talk about time-to-failure models. Epidemiologists might talk about survival models. In all cases, we’re trying to make predictions about the time until a particular event – failure of a key mechanical part, or death due to disease

a mathematical system that undergoes transitions from one state to another, between a finite or countable number of possible states. It is a random process characterized as memoryless: the next state depends only on the current state and not on the sequence of events that preceded it. This specific kind of "memorylessness" is called the Markov property. Markov chains have many applications as statistical models of real-world processes.

In this article I'm describing the math behind it. Don't fear the math, as this is simple enough that a high-schooler understands. And even though there are a lot of libraries out there that already do this, you're far better off for understanding the concept behind it, otherwise you won't be able to tweak the implementation in response to your needs.

from Statistical Modeling, Causal Inference, and Social Science http://andrewgelman.com

So how might we go about simulating a harmonograph? Well the motion of a single damped pendulum along the x axis can be described by the parametric equation

each variable can take one of several discrete values, or the range of possible values is divided to give a finite number of possibilities. Taking the variables together, a huge number of combinations of values must be considered. This effect is also known as the combinatorial explosion.

Game theory attempts to mathematically capture behaviour in strategic situations, in which an individual's success in making choices depends on the choices of others

Logical literacy is essential to mathematical fluency.

Logical literacy is an awareness and understanding of the metalanguage in which propositions, conjectures, lemmas and theorems are written.

Learning how to read this metalanguage is not hard; and once it's learned, it becomes possible to tease out and translate (perhaps slowly at first) the main ideas in a technical paper.

Discrete mathematical structures form the foundation of computer science.

These structures are so universal that most research papers in the theory of computation, programming languages and formal methods present concepts in terms of discrete mathematics rather than code.

Logistic regression takes into account prior performance. So, getting lots correct is always a good thing, and you’ll be able to recover faster from a wrong answer if you were previously doing well. Contrast with the streak model, which loses all memory after a single incorrect answer.

caused me to wonder whether it was possible to have a consistent philosophy of data analysis and whether it could it be possible that Godel’s incompleteness theorem extends as far as to say that it wasn’t possible?

'My objective is to get up to the white on white and still be alive.' As of July 2004, he had reached 5.5 million. Adopting this rigorously serialized approach, Opałka aligned himself with many other artists of the time who explored making art through systems and mathematics

"One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In particular, I argue that computational complexity theory---the field that studies the resources (such as time, space, and randomness) needed to solve computational problems---leads to new perspectives on the nature of mathematical knowledge

Lecture by Professor Andrew Ng for Machine Learning (CS 229) in the Stanford Computer Science department. Professor Ng provides an overview of the course in this introductory meeting.

This course provides a broad introduction to machine learning and statistical pattern recognition. Topics include: supervised learning (generative/discriminative learning, parametric/non-parametric learning, neural networks, support vector machines); unsupervised learning (clustering, dimensionality reduction, kernel methods); learning theory (bias/variance tradeoffs; VC theory; large margins); reinforcement learning and adaptive control

An example of a stochastic process in discrete time would be the sequence of temperatures recorded every morning at Braemar in the Scottish Highlands. Another example would be the price of a share recorded at the opening of the market every day. During the day we can trace the share price continuously, which would constitute a stochastic process in continuous time.

This is the first textbook on pattern recognition to present the Bayesian viewpoint. The book presents approximate inference algorithms that permit fast approximate answers in situations where exact answers are not feasible. It uses graphical models to describe probability distributions when no other books apply graphical models to machine learning.

Instead of taking a linguistic expression as something that requires decoding, Google Translate (GT) takes it as something that has probably been said before.<br />
<br />
It uses vast computing power to scour the internet in the blink of an eye, looking for the expression in some text that exists alongside its paired translation.

In this course we will cover central aspects of modern formal logic, beginning with an explanation of what constitutes good reasoning. Topics will include validity and soundness of arguments, formal derivations, truth-functions, translations to and from a formal language, and truth-tables. We will thoroughly cover sentential calculus and predicate logic, including soundness and completeness results.

fast, flexible, and expressive data structures designed to make working with “relational” or “labeled” data both easy and intuitive. It aims to be the fundamental high-level building block for doing practical, real world data analysis in Python. Additionally, it has the broader goal of becoming the most powerful and flexible open source data analysis / manipulation tool available in any language.

algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as, for example, index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings.

This website is about your choices if you wish to start studying mathematics with the Open University. It describes courses and possible study routes, and gives you information which you might take into consideration when making your decision. It also gives you help in judging which of the possible routes is best for you.

Graph theory is a fundamental area of study in discrete mathematics. As the name implies graph theory is about graphs, so I’ll first define graph and then discuss why people are so interested in studying these critters.

In the first and second parts of my series on graph theory I defined graphs in the abstract, mathematical sense and connected them to matrices. In this part we’ll see a real application of this connection: determining influence in a social network.

a python package providing convenient data structures for time series, cross-sectional, or any other form of “labeled” data, with tools for building statistical and econometric models.

Dan Meyer has linked to some of the best papers he's been reading at grad school. If you have opinions about education, or are thinking of doing something to "fix education", you have to read Public Goods, Private Goods

The purpose of this chapter is to provide the reader with an overview over the vast range of applications which have at their heart a machine learning problem and to bring some degree of order to the zoo of problems.

probability and statistics textbook, for maths students to build up to understanding Bayesian reasoning.

RStudio brings together everything you need to be productive with R in a single, customizable environment.

We focus on the news domain: given two news articles, our system automatically finds a coherent chain linking them together.

The first skill, as you might expect, is a base in statistics, algorithms, machine learning, and mathematics. "You need to have a solid grounding in those principles to actually extract signals from this data and build things with it,"

techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps us understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed.

It's a world away from where Stonebraker started. In addition to being multi-dimensional and offering array based scaling from megabytes to petabytes and running on tens of thousands clustered nodes, SciDB's will be write once read many, allow bulk load rather than single road insert, provide parallel computation, be designed for automatic rather than manual administration, and work with R, Matlab, IDL, C++ and Python.

Welcome to Q&A for people studying math at any level and professionals in related fields

Punk Mathematics will be a series of mathematical stories. It is written for readers who are interested in having their minds expanded by the strange metaphors and implications of mathematics, even if they're not always on friendly terms with equations

In much the same way that imperative mood in natural languages expresses commands to take action, imperative programs define sequences of commands for the computer to perform.

It is a collection of definitions, postulates (axioms), propositions (theorems and constructions), and mathematical proofs of the propositions. The thirteen books cover Euclidean geometry and the ancient Greek version of elementary number theory.

We developed a generalized framework of network quality functions that allowed us to study the community structure of arbitrary multislice networks, which are combinations of individual networks coupled through links that connect each node in one network slice to itself in other slices. This framework allows studies of community structure in a general setting encompassing networks that evolve over time, have multiple types of links (multiplexity), and have multiple scales.

This library provides a set of tools for drawing graphs in 2D or 3D. We have developed the library in order to be able to use processing for simple scientific simulations or data displays.

Learn from academic literature about how the mapreduce parallel model and hadoop implementation is used to solve algorithmic problems.

James Montgomery, a Wisconsin soc prof/econ PhD, has a very nice website with his math soc course notes. The lectures will be a text book. I say it hits the right note. It has classical math soc, like influence models and Markov chains, but newer stuff like cultural evolution models and segregation dynamics.

The question of what computer science can teach social science disciplines such as economics is a constant discussion here at Michigan CSCS. I would say the consensus is that there exists real opportunities for meaningful cross-fertilization.

Even if you're not into visualization, you're going to need at least a subset of the skills that Fry highlights if you want to seriously mess with data. Statisticians should know APIs, databases, and how to scrape data; designers should learn to do things programmatically; and computer scientists should know how to analyze and find meaning in data.

Multiplication is a wonderful little operation. Depending on the context, it can

Elegant, “a ha!” insights should be our focus, but we leave that for students to randomly stumble upon themselves. I hit an “a ha” moment after a hellish cram session in college; since then, I’ve wanted to find and share those epiphanies to spare others the same pain.

Abstract: Graph mining and network analytics is critical to a variety of application domains, ranging from community detection in social networks, malicious program analysis in computer security, to searches for functional modules in biological pathways and structural analysis in chemical compounds. There is an emerging need to systematically investigate the modeling, managing, and mining of large-scale graphs and networks in bioinformatics, social networks, and computer systems. In this seminar, we are going to discuss the state-of-the-art research results and identify potential topics for graduate research in graph mining.

Nash himself gives an articulate account of his own illness and how society deals with those who experience other realities, while the documentary traces Nash's sometimes less-than-flattering earlier life story to his later years where he is widely considered to be an altogether more gentle and humane individual.

Is Graziano's math arising out of the natural world, or is it imposed upon it? I don't know whether she's doing something profound, or just being clever, and this ambiguity bothers me. But it has made me think, and that's certainly the function of art.

’ll be writing about the elements of mathematics, from pre-school to grad school, for anyone out there who’d like to have a second chance at the subject — but this time from an adult perspective. It’s not intended to be remedial.

"The next sentence is false. The previous sentence is true."

With equal passion I have sought knowledge. I have wished to understand the hearts of men. I have wished to know why the stars shine. And I have tried to apprehend the Pythagorean power by which number holds sway about the flux. A little of this, but not much, I have achieved.

Prover9 is an automated theorem prover for first-order and equational logic, and Mace4 searches for finite models and counterexamples. Prover9 is the successor of the Otter prover.

Costello's research continues but what seems clear to me is that a system that is claimed to be foolproof has inbuilt flaws that are beginning to take effect when there are just 4.3m samples on record. What happens if there are 60m samples on the NDNAD? And what about the profiles of innocent people kept by this appalling government despite the European court's ruling?

Sanborn named his proposal after the Greek word for hidden. The work is a meditation on the nature of secrecy and the elusiveness of truth, its message written entirely in code.

The use of geo-aware peer-to-peer query strings presents a potentially major shift in music hit-prediction software, most of which — like Hit Song Science  — collects data on the sound of a song, then compares the melody, tempo, and lyrics for example of a potential hit to a database of established hits. "Our algorithm never hears the actual song; it is based on the Internet mirroring of the social word of mouth of people spreading their interest in the song," says Shavitt. "It will be interesting to compare the success rates of both approaches."

The concept of aleph-1 derives from the theories of the mathemtician Georg Cantor, who was teaching in halle, germany, a city, to which Nicolai is deeply connected with through his family.
The sound pieces of aleph-1 deal with the idea of infinity in terms of structure and length. Without actual beginning or end, they fade in and out.

n mathematics, a Lissajous curve (Lissajous figure or Bowditch curve) is the graph of the system of parametric equations

x=A\sin(at+\delta),\quad y=B\sin(bt),

which describes complex harmonic motion. This family of curves was investigated by Nathaniel Bowditch in 1815, and later in more detail by Jules Antoine Lissajous (pronounced LEE-suh-zhoo) in 1857.

Last week, I stumbled upon the amazing paper by Godfried Toussaint called The Euclidean Algorithm Generates Traditional Musical Rhythms, which shows how the euclidean algorithm used for example for timing systems in neutron accelerators can generate most of the traditional european and african rhythms.

Social dynamics is the study of the ability of a society to react to inner and outer changes and deal with its regulation mechanisms. Social dynamics is a mathematically inspired approach to analyse societies, building upon systems theory and sociology.

The following list was prepared by Alan Kay for his students and is presented here for those who want to learn more about the ideas that influenced Etoys.

When you enable Mail Goggles, it will check that you're really sure you want to send that late night Friday email. And what better way to check than by making you solve a few simple math problems

In the Internet age, once you learn the basic core material, perhaps the best way to direct the growth of learning is to chase down real-world problems and fix them. You learn how to wrestle with failure, and how to get the resources you need.

By showing that the world could be described mathematically, Pythagoras not only provided an important inspiration for physics, but he also discovered a particular affinity between mathematics and music

This thread is for collecting together postings of all links related to DSP theory and practice information, with a particular focus on "DSP for dummies" websites. Any other links related to things like: "math for DSP", "FFT theory and applications", "dig

Mathematics is objective, exact and scientific. Music is subjective, creative and emotional. Yet, from classical composers to computers, the two have been linked together for centuries.

Whereas most rock music uses a basic 4/4 beat (however accented or syncopated), math rock frequently uses asymmetrical time signatures such as 7/8, 11/8, or 13/8, or features constantly changing meters based on various groupings of 2 and 3.

That beauty was richly on display at an exhibition of mathematical art at the Joint Mathematics Meetings in San Diego in January, where more than 40 artists showed their creations.

simply a state machine is a model of behavior composed of a finite number of states, transitions between those states, and actions

Wolfram likens the study of the universe of possible programs to many classic explorations in science--including the exploration of possible chemicals and of possible biological species.

Wolfram likens the study of the universe of possible programs to many classic explorations in science--including the exploration of possible chemicals and of possible biological species.

Streaming video: Language Evolution

"We measured something no one really thought could be measured, and got a striking and beautiful result."